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Operations Research Transactions ›› 2023, Vol. 27 ›› Issue (3): 109-120.doi: 10.15960/j.cnki.issn.1007-6093.2023.03.008

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Analysis of waiting time of customers in an M/M/c/m + c queueing system with customer interjections

Wenqing WU1,2,(), Qilin KE3, Yinghui TANG3, Lin CHEN4   

  1. 1. School of Science, Civil Aviation Flight University of China, Deyang 618307, Sichuan, China
    2. School of Mathematics and Physics, Southwest University of Science and Technology, Mianyang 621010, Sichuan, China
    3. School of Mathematical Sciences, Sichuan Normal University, Chengdu 610068, Sichuan, China
    4. College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400067, China
  • Received:2020-12-11 Online:2023-09-15 Published:2023-09-14
  • Contact: Wenqing WU E-mail:wwqing0704@swust.edu.cn

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Abstract:

This paper studies waiting time distributions of customers in a multi-server queueing system with customer interjections and finite buffer. The customers who enter the system are divided into regular customers and interjection customers according to whether they interject the queue or not. After entering the system, the regular customers queue up at the end of the waiting line and wait for service, while the interjection customers queue up as close as possible to the head of the waiting line to receive service. By using the properties of negative exponential distribution and phase type distribution, the matrix expressions of waiting time distribution of customers in waiting queue position $n$, regular customers and interjection customers are derived. Further, the plots of waiting time distributions with time $t$ are given.

Key words: $M/M/c/m+c$ queueing system, customer interjection, the function of the waiting time distribution, phase type distribution

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